Study of the reconstruction method of distribution of relaxation times of electrochemical impedance spectroscopy based on elastic net regularization

doi:10.11949/0438-1157.20231079

Abstract

Abstract:

Electrochemical impedance spectroscopy (EIS) has a wide range of applications in the research of fuel cells and secondary batteries. Distribution of relaxation times (DRT) is a novel and efficient EIS analysis technique, which has the advantages of not relying on prior knowledge and high resolution. However, the reconstruction process of the DRT function is an inverse problem solving process, and there are ill-posed problems. In response to the above challenges, an innovative DRT function reconstruction method combining elastic network regularization and quantum-behaved particle swarm optimization algorithm is proposed. The ill-posed problem can be effectively solved by the elastic network regularization, while the regularization parameters (regularization factor and mixing coefficient) of the elastic net regularization can be reasonably selected by the quantum particle swarm algorithm, avoiding the problem of manual parameter selection. The reliability of the developed DRT reconstruction method was evaluated by using EIS of equivalent circuits, EIS of equivalent circuits containing noise, and EIS of experimental measurements. The results indicate that the developed DRT reconstruction method can reconstruct high-quality DRT functions in all three cases.

Key words: electrochemical impedance spectroscopy, distribution of relaxation times, fuel cells, elastic net regularization, quantum-behaved particle swarm optimization algorithm

摘要：

电化学阻抗谱（EIS）在燃料电池和二次电池研究中有广泛的应用，弛豫时间分布（DRT）是一种新型和高效的EIS解析技术，其具有不依赖于先验知识和分辨率高等优点。但DRT函数的重构过程是一个反问题求解过程，并存在不适定问题。针对上述难题，提出一种结合弹性网正则化和量子粒子群算法的DRT函数重构方法，其中弹性网正则化可有效解决不适定问题，而量子粒子群算法可以合理选择弹性网正则化的参数（正则化因子和混合系数），避免了人工选择参数的问题。分别采用等效电路的EIS、包含噪声的等效电路EIS和实验测量的EIS，考察所开发DRT重构方法的可靠性。研究结果表明：所开发的DRT重构方法在上述三种情况下均可以重构出高质量DRT函数。

关键词: 电化学阻抗谱, 弛豫时间分布, 燃料电池, 弹性网正则化, 量子粒子群算法

CLC Number:

O 646

Qun ZHENG, Xuzhao WEI, Lexian DONG, Jihao ZHANG, Libin LEI. Study of the reconstruction method of distribution of relaxation times of electrochemical impedance spectroscopy based on elastic net regularization[J]. CIESC Journal, 2023, 74(12): 4979-4987.

郑群, 魏旭钊, 董乐贤, 张纪豪, 雷励斌. 基于弹性网正则化的电化学阻抗谱弛豫时间分布重构方法的研究[J]. 化工学报, 2023, 74(12): 4979-4987.

Figures/Tables 7

Fig.1 Flow diagram of reconstruction DRT functions combing elastic net regularization and quantum-behaved particle swarm optimization algorithm

Fig.2 The effect of regularization parameter (λ) and mixing parameter (L1ratio) on DRT and MSE

Table 1 Parameters of equivalent circuit

电化学元器件	参数值	特征弛豫时间 $(τ = R C)$	特征频率 $f = 1 2 π τ$
$R 0$	0.860 Ω
$R 1$	$0.154 Ω$	$1.380 × 10 - 1 s$	$1.153 H z$
$C 1$	$9.00 × 10 - 1$ F	$1.380 × 10 - 1 s$	$1.153 H z$
$R 2$	0.269 $Ω$	$8.877 × 10 - 3 s$	$17.929 H z$
$C 2$	$3.30 × 10 - 2$ F	$8.877 × 10 - 3 s$	$17.929 H z$
$R 3$	0.13 $8 Ω$	$2.900 × 10 - 3 s$	$54.881 H z$
$C 3$	$2.10 × 10 - 2$ F	$2.900 × 10 - 3 s$	$54.881 H z$

Table 1 Parameters of equivalent circuit

电化学元器件	参数值	特征弛豫时间 $(τ = R C)$	特征频率 $f = 1 2 π τ$
$R 0$	0.860 Ω
$R 1$	$0.154 Ω$	$1.380 × 10 - 1 s$	$1.153 H z$
$C 1$	$9.00 × 10 - 1$ F	$1.380 × 10 - 1 s$	$1.153 H z$
$R 2$	0.269 $Ω$	$8.877 × 10 - 3 s$	$17.929 H z$
$C 2$	$3.30 × 10 - 2$ F	$8.877 × 10 - 3 s$	$17.929 H z$
$R 3$	0.13 $8 Ω$	$2.900 × 10 - 3 s$	$54.881 H z$
$C 3$	$2.10 × 10 - 2$ F	$2.900 × 10 - 3 s$	$54.881 H z$

Fig.3 Reconstruction DRT function combing elastic net regularization and QPSO algorithm

Fig.4 The effect of internal parameters of QPSO algorithm on DRT function

Fig.5 Reconstruction of DRT functions from EIS with noise

Fig.6 Reconstruction of DRT function from experimental EIS data

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